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Finding the Third Proportional to 3,204 and 4,046

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Solution

The third proportional to 3,204 and 4,046 is: 5,109.27

Step by Step Solution

  1. Step 1: Write the proportion equation
    3,204 : 4,046 = 4,046 : x
  2. Step 2: Convert to fraction form
    3,204/4,046 = 4,046/x
  3. Step 3: Cross multiply
    3,204x = 4,046 × 4,046
  4. Step 4: Simplify right side
    3,204x = 16,370,116
  5. Step 5: Solve for x
    x = 16,370,116/3,204
  6. Step 6: Final answer
    x = 5,109.27

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Why These Related Problems?

These problems maintain the same ratio (1.26) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.